Damage

Core
Core damage is indicated by grey numbers and is damage dealt directly to a Behemoth's health pool. It is the main way of killing a Behemoth. While other damage types do not damage the health pool, base damage is still being dealt in the background while dealing damage to break points - the number is simply hidden in favour of showing part damage.

Part
Part damage is the damage dealt to unbroken parts of a Behemoth and is indicated by yellow numbers. This damage does not directly damage a Behemoth's actual health pool, and only counts towards the damage threshold for breaking a part. Once that threshold is reached, that part will break off from a Behemoth as a lootable item and no longer take part damage, the behemoth will also be stunned for a short duration.

Breaking parts can alter a Behemoth's attacks and behavior, most often when severing the tail. One example of these changes that occur is Charrogg, who has unique parts to break off - his blaze vents - that prevent him from spewing out fire during certain moves.

All weapons can deal part damage, but slashing weapons (Sword, Axe, War Pike, and Chain Blades) have a +50% part damage bonus when attacking Behemoth tails or other severables.

Cells that increase or deal part damage include Bladestorm and Sharpened.

Stagger
Stagger damage is damage dealt to a Behemoth's head or legs and allows slayers to stagger, stun or knockdown Behemoths. Stagger damage is indicated by blue damage numbers and does not affect the Behemoth's basic health pool. Generally, hitting the head of a Behemoth deals higher stagger damage than impact to the legs, but can vary between different Behemoths.

This is primarily dealt by slashing (Sword, Axe, and Chain Blades) and blunt (Hammer and Aether Strikers) weapons, with blunt-types dealing a higher base amount of stagger damage. There is a minimum damage threshold that must be met to deal stagger damage, so often a lower damage-dealing weapon like Chain Blades will not deal stagger damage when attacking.

Cells that increase or deal stagger damage include Knockout King, Pacifier, and Weighted Strikes.

Wound
Wound damage will create wounded points on a Behemoth's body where part damage can be dealt (i.e. legs, tail, and head), regardless of break status. This damage type is indicated by red numbers and does not affect the Behemoth's basic health pool.

Once a wound has been created the wounding party will receive the Aether Rush buff (15% bonus to Attack Damage, Attack Speed, Movement Speed and Stamina Regeneration for 20 seconds). This can also be earned by dealing a total of 1500 damage to wounded parts across any number of wounded parts. Wounded parts will remain wounded for a total of 15 seconds.

Piercing weapons (War Pike) have the innate ability to apply and deal wound damage.

Cells that increase or deal wound damage include Acidic, Barbed, and Merciless.

In-Depth
Welcome to the In-depth part of this page. Here you will find approximate calculations to different kinds of damage.

Core/Health
The Core/Health of a Behemoth can be calculated with this formula:

Part Damage
The Part damage can be calculated with:

Stagger Damage
The Stagger, one of the most essential types of damage during a hunt. You can calculate this with this formula:

Wound Damage
Wound being a part of any assists role. You can calculate this with this formula:

Attack Types
Different weapons, and attacks from those weapons can deal different types of damage, these provide the  values seen above and cannot be directly changed. The severables below include tails and horns while the armour is the plating found on the Skarn or Torgadoro's gloved fists.

Slashing
Dealt by the Axe, Sword, and Chain Blades, as well as War Pike heavy, slashing, attacks.
 * 100% Core Damage
 * 100% Part Damage
 * 100% Base Stagger Damage
 * 0% Base Wound Damage
 * +50% Part Damage to severables
 * Can sever parts
 * 75% Part Damage to Armour

Blunt
Dealt by the Hammer and Aether Strikers.
 * 100% Core Damage
 * 100% Part Damage
 * 133.33% Base Stagger Damage
 * 0% Base Wound Damage
 * Can sever parts
 * 100% Part Damage to Armour

Piercing
Dealt purely by the War Pike light, stabbing, attacks.
 * 100% Core Damage
 * 100% Part Damage
 * 0% Base Stagger Damage
 * 133% Base Wound Damage
 * +25% Part Damage to severables
 * Can sever parts
 * 75% Part Damage to Armour

Shot
Dealt by Ostian Repeaters and the Adamant Bolt Special.
 * 100% Core Damage
 * 100% Part Damage
 * 0% Base Stagger Damage
 * 0% Base Wound Damage
 * Can sever parts
 * 75% Part Damage to Armour

Special/AoE
Used by certain special effects sure as Volatile Axecore and Sword Overdrive Slicers for a full list see the original work.
 * 100% Core Damage
 * Part Damage inherited from the weapon used, Slashing for War Pikes
 * No Stagger Damage
 * No Wound Damage
 * Not affected by Part Damage buffs
 * Not affected by single hit buffs
 * Not counted for hit counting effects (Such as the Hellion Unique Effect)
 * Not affected by Marksman
 * Armour Damage inherited from the weapon used, Slashing for War Pikes

Item
Dealt by Lanterns attacks, Grenades and Airstrikes, as well as Escalation Amps such as Eidolons. This is affected only by power and does not have it's own elemental bonuses, or penatlies.
 * 100% Core Damage
 * 100% Part Damage
 * No Stagger Damage
 * No Wound Damage
 * 100% Part Damage to Armour

Credits
All of these calculations were found by Ket & Froogal.